WASHINGTON – The Senate unanimously agreed yesterday that strengthening Social Security was “a vital national priority” but split acrimoniously along party lines on what to do about it in the first votes on President Bush’s plans.

In one exception to the party divide, five Republicans broke ranks and voted with the Democrats in favor of a resolution declaring, “Congress should reject any Social Security plan that requires deep benefit cuts or a massive increase in debt.”

Democrats argue that Mr. Bush cannot establish private investment accounts, his signature proposal for revamping the retirement program, without cutting benefits or adding to the federal budget deficit.

“They’re nervous. They’re worried. But their hands are tied as long as the president sticks to privatization,” said Senator Schumer of New York, the top Democratic spokesman on the issue in the Senate.

The vote on the resolution, offered by Senator Nelson, a Democrat of Florida, was 50-50, with Republicans Susan Collins and Olympia Snowe of Maine, Mike DeWine of Ohio, Lindsey Graham of South Carolina, and Arlen Specter of Pennsylvania joining with the chamber’s Democratic minority.

Senate Budget Committee Chairman Judd Gregg, a Republican of New Hampshire, told Democrats that rather than offering a plan for overhauling the giant pension program, “You just put out there amendments which are for the purposes of political protection. You should be ashamed of yourselves.”

The resolutions voted on yesterday were nonbinding but symbolic of where the issue stands.

All 100 senators voted in favor of another resolution offered by Mr. Graham, who has sought bipartisan compromise on the issue, that pointedly avoided referring to Social Security’s financial state as a “crisis,” a term which Mr. Bush has used to objections by Democrats.

The provision said lawmakers “should work together at the earliest opportunity to enact legislation to achieve a solvent and permanently sustainable Social Security system.” It omitted details of how the program would be reshaped.

In a purely partisan 55-45 vote, the senators rejected an amendment offered by Senator Conrad, a Democrat of North Dakota, that would have made it virtually impossible for the body to consider any spending or tax legislation until Social Security’s long-term solvency is assured.

By a margin of 56-43, senators approved a provision by Senator DeMint, a Republican of South Carolina, that was similar to Mr. Nelson’s but added that failure to address Social Security’s ills would trigger “massive debt, deep benefit cuts and tax increases.” On that resolution, three Democrats voted with the Republicans – Mr. Nelson, Robert Byrd of West Virginia, and Ben Nelson of Nebraska – while two Republicans voted with the Democrats – Ms. Snowe and Senator Voinovich of Ohio.

The votes came hours after a subcommittee meeting in which Senator Clinton clashed with Alan Greenspan over rosy surplus forecasts the Federal Reserve chairman relied on to support Mr. Bush’s 2001 tax cuts. The estimates turned out to be considerably off the mark. “It turns out that we were all wrong,” Mr. Greenspan said.

“Just for the record, we were not all wrong, but many people were wrong,” Mrs. Clinton, a Democrat of New York, quickly shot back.

Mr. Greenspan lent critical support for Mr. Bush’s first-term tax cuts, saying they would stimulate the then-ailing economy. Mr. Clinton and many Democrats voted against the tax cuts, arguing that they would mainly benefit the wealthy and that federal deficits would balloon. They have issued similar warnings about the president’s Social Security proposal.

Mr. Greenspan said that in early 2001, “we were confronted at that time with an almost universal expectation amongst the experts that we were dealing with a very large surplus for which there seemed to be no end.”

The federal government did produce a budget surplus in 2001. But since then, it has been racking up record amounts of red ink.

The Fed chairman, however, didn’t retract his support for the 2001 tax cut.

“If confronted with the same evidence we had back then, I would recommend exactly what I recommended then,” Mr. Greenspan said.

In his testimony, Mr. Greenspan again endorsed a key part of Mr. Bush’s Social Security overhaul – private investment accounts. “We should start very slowly and see whether or not it is disruptive,” he said. “If it is, we had better very quickly reverse course.”

The Congressional Budget Office also released a new analysis of the president’s budget proposal, and it estimated that if all Americans signed up for the accounts as outlined by Mr. Bush, it would cost $969 billion from 2009 to 2015.